Search results for "Mathematica"
showing 10 items of 7971 documents
Boundary value problem with integral condition for a Blasius type equation
2016
The steady motion in the boundary layer along a thin flat plate, which is immersed at zero incidence in a uniform stream with constant velocity, can be described in terms of the solution of the differential equation x'''= -xx'', which satisfies the boundary conditions x(0) = x'(0) = 0, x'(∞) = 1. The author investigates the generalized boundary value problem consisting of the nonlinear third-order differential equation x''' = -trx|x|q-1x'' subject to the integral boundary conditions x(0) = x'(0) = 0, x'(∞) = λ∫0ξx(s) ds, where 0 0 is a parameter. Results on the existence and uniqueness of solutions to boundary value problem are established. An illustrative example is provided.
Multi-parameter analysis of the obstacle scattering problem
2022
Abstract We consider the acoustic field scattered by a bounded impenetrable obstacle and we study its dependence upon a certain set of parameters. As usual, the problem is modeled by an exterior Dirichlet problem for the Helmholtz equation Δu + k 2 u = 0. We show that the solution u and its far field pattern u ∞ depend real analytically on the shape of the obstacle, the wave number k, and the Dirichlet datum. We also prove a similar result for the corresponding Dirichlet-to-Neumann map.
ENVIRONMENTAL FOOTPRINT REDUCTION FOR WASTEWATER TREATMENT BY MULTI-OBJECTIVE OPTIMIZATION AND MODELLING
2020
The current challenge faced by researchers and managers is minimize the environmental footprint of wastewater treatment plants (WWTPs). To accomplish this goal, other than respect legal requirements, WWTPs must provide better responses regarding consumption of energy and resources, greenhouse gas (GHG) emissions, among others. The research hereby presented is based on the application of mathematical modelling with the aim to propose a framework for the minimization of WWTP’s environmental footprint towards optimization techniques. A literature review was held to gain knowledge regarding the main decision support systems (DSS) that are applied to WWTPs since they allow selecting the most app…
Monitoring and data quality assessment of the ATLAS liquid argon calorimeter
2014
The liquid argon calorimeter is a key component of the ATLAS detector installed at the CERN Large Hadron Collider. The primary purpose of this calorimeter is the measurement of electron and photon kinematic properties. It also provides a crucial input for measuring jets and missing transverse momentum. An advanced data monitoring procedure was designed to quickly identify issues that would affect detector performance and ensure that only the best quality data are used for physics analysis. This article presents the validation procedure developed during the 2011 and 2012 LHC data-taking periods, in which more than 98% of the proton-proton luminosity recorded by ATLAS at a centre-of-mass ener…
Partial data inverse problems and simultaneous recovery of boundary and coefficients for semilinear elliptic equations
2021
We study various partial data inverse boundary value problems for the semilinear elliptic equation $\Delta u+ a(x,u)=0$ in a domain in $\mathbb R^n$ by using the higher order linearization technique introduced in [LLS 19, FO19]. We show that the Dirichlet-to-Neumann map of the above equation determines the Taylor series of $a(x,z)$ at $z=0$ under general assumptions on $a(x,z)$. The determination of the Taylor series can be done in parallel with the detection of an unknown cavity inside the domain or an unknown part of the boundary of the domain. The method relies on the solution of the linearized partial data Calder\'on problem [FKSU09], and implies the solution of partial data problems fo…
Global Dynamics and Imbalance Effects in the Lucas-Uzawa Model: Further Results
2007
In this paper we use a new analytical approach to the Lucas-Uzawa model (Boucekkine and Ruiz Tamarit, 2007) to extend the existing results on the dynamics, and notably on the imbalance effects arising in the model. The approach does not only allow to extend the traditional analysis to any initial conditions and for all variables in level, but it also permits a more general investigation of imbalance effects.
A strategic approach for the discounted Shapley values
2014
The family of discounted Shapley values is analyzed for cooperative games in coalitional form. We consider the bargaining protocol of the alternating random proposer introduced in Hart and Mas-Colell (Econometrica 64:357–380, 1996). We demonstrate that the discounted Shapley values arise as the expected payoffs associated with the bargaining equilibria when a time discount factor is considered. In a second model, we replace the time cost with the probability that the game ends without agreements. This model also implements these values in transferable utility games, moreover, the model implements the \(\alpha \)-consistent values in the nontransferable utility setting.
Solidarity in games with a coalition structure
2010
Abstract A new axiomatic characterization of the two-step Shapley value Kamijo (2009) is presented based on a solidarity principle of the members of any union: when the game changes due to the addition or deletion of players outside the union, all members of the union will share the same gains/losses.
Effets de quartier, effet de département : discrimination liée au lieu de résidence et accès à l'emploi
2013
L’objet de cette étude est de mesurer la discrimination à l’embauche à l’encontre des jeunes en Ile-de-France en raison du lieu de résidence en considérant plusieurs échelles spatiales de façon à distinguer l’effet de la réputation du département (Paris et la Seine-Saint-Denis), celui de la localité et celui du quartier. L’évaluation est réalisée sur données expérimentales auto-construites de testing selon un protocole permettant d’examiner les effets propres à chacune de ces trois échelles sur l’accès à l’emploi ainsi que leurs effets cumulés. On s’intéresse aux discriminations pour deux professions en tension du secteur de la restauration pour laquelle les discriminations devraient a prio…
Chaos and its Degradation-Promoting-Based Control in an Antithetic Integral Feedback Circuit
2022
This letter deals with a novel variant of antithetic integral feedback controller (AIFC) motifs which can feature robust perfect adaptation, a pervasive (desired) ability in natural (synthetic) biomolecular circuits, when coupled with a wide class of process networks to be regulated. Using the separation of timescales in the proposed kind of AIFC, here we find a reducedorder controller that captures the governing slow part of the original solutions under suitable assumptions. Inspired by R(ossler systems, we then make use of such a simpler controller to show that the antithetic circuit can exhibit chaotic behaviors with strange attractors, where the bifurcation from a homeostatic state to c…